We introduce the concepts of interval-valued fuzzy mα-open sets and interval-valued fuzzy mα-continuous mappings. And we study some characterizations and properties of such concepts.

This note concerns subsets A of the unit 2-sphere 5 such that (*) for each continuous real-valued mapping/ of 5 there exists a rotation r of S with all points of r(A) having the same value under/. In 1942, Kakutani [3 ] proved that the set A of end points of an orthonormal set of 3 vectors has property (*). It was observed by de Mira Fernandes [5 ] that the same proof holds in case A is the set...

In this paper, we introduce the Choquet-Pettis integral of set-valued mappings and investigate some properties and convergence theorems for the set-valued Choquet-Pettis integrals.

In this paper, we introduce the Pettis integral of fuzzy mappings in Banach spaces using the Pettis integral of closed set-valued mappings. We investigate the relations between the Pettis integral, weak integral and integral of fuzzy mappings in Banach spaces and obtain some properties of the Pettis integral of fuzzy mappings in Banach spaces.

We introduce the concepts of IVF m-semiopen sets, IVF m-preopen sets, IVF m-semicontinuous mappings and IVF mprecontinuous mappings on interval-valued fuzzy minimal spaces. We investigate characterizations of IVF m-semicontinuous mappings and IVF m-precontinuous mappings and study properties of IVF m-semiopen sets and IVF m-preopen sets.

Some coincidence and fixed point theorems are proved for certain generalized contraction type single-valued and set-valued compatible mappings. 2000 Mathematics Subject Classification. 47H10, 54H25.

The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...

The concept of equi-outer semicontinuity allows us to relate the pointwise and the graphical convergence of set-valued-mappings. One of the main results is a compactness criterion that extends the classical Arzelà-Ascol̀ı Theorem for continuous functions to this new setting; it also leads to the exploration of the notion of continuous convergence. Equi-lower semicontinuity of functions is relate...

A new class of nonlinear set-valued variationalinclusions involving $(A,eta)$-monotone mappings in a Banachspace setting is introduced, and then based on the generalizedresolvent operator technique associated with$(A,eta)$-monotonicity, the existence and approximationsolvability of solutions using an iterative algorithm and fixedpint theory is investigated.

In this paper, existence theorems for the fuzzy Volterra-Fredholm integral equations of mixed type (FVFIEMT) involving fuzzy number valued mappings have been investigated. Then, by using Banach's contraction principle, sufficient conditions for the existence of a unique solution of FVFIEMT are given. Finally, illustrative examples are presented to validate the obtained results.